So, the current in-game day is November 3rd, 2156, and I just got back from contacting the Sylandro after nearly six months of travel. Once I got back, I was told by Commander Hayes that there was something at Hyperspace coordinates 100 : 50, or something like that.

Though I saved and exited the game immediately after that. When I came back, I can no longer access his piece of dialouge, and when I went to those coordinates in Hyperspace, nothing was there.

Firstly, since I suspect you may be doing your first playthrough, know that the below answer may contain spoilers.

Now, those coordinates seem to practically point towards Epsilon Giclas, which would be within the sphere of influence of a certain alien race. The Pkunk, if you don't mind direct spoilers. Judging by the fact that you don't seem to be aware of their (former) presence there, they aren't on your starmap. They should be heading 'east' on the starmap - if you're not too late already, you might be able to intercept them before they reach the Serpentis stars and disappear. Of course, considering how long you were away it's possible that they almost crossed the entire distance before you came back to base, in which case there's not much you can do, but hopefully that's not the case. I'd recommend heading for the Gorno constellation -or, if that fails, Capella- and from there you can start slowly heading west whilst looking for hyperspace blips. If you still fail to catch anything, head back to the starbase - Hayes might have another message in store for you then, and if not, you probably just missed them.

"Sentient life. We are the Ur-Quan. Independence is intolerable. Blah, blah, blah." - the Spathi High Council, Star Control II.

It sounds like you didn't get a chance to actually read what Commander Hayes said, so here's a transcript:

We have detected a minute but measurable disturbance in the InterSpace fabric
at approximate TrueSpace coordinate 100:50.
Our scientists speculate that this disturbance may be caused by many thousands of HyperWarp penetrations
all in phase -- as though a huge fleet of ships were on the move.

It's exactly what Hayes says it is; there's a massive fleet of ships on the move at that location. Check your Starmap; do you notice anything unusual?